Predictive Formulation for the Ultimate Combinations of Axial Force and Bending Moment Attainable by Steel Members

This paper is devoted to quantitative safety assessment of steel beam-columns, and delivers a plain analytical formulation for predicting the ultimate combinations of axial force and bending moment, allowing for material and geometric non-linearities. The formulation easily permits the ultimate interaction diagram of a steel member to be accurately constructed, as well as the structure to be checked for combined axial force and lateral load. It applies specifically to columns but can be used for any members. The formulation is also configured as a tool for straightforward design and construction. To that end, the structure is converted from an imperfect geometrically non-linear system into a geometrically linear system without imperfections, which allows the structure to be designed and dimensioned referring to the first order moments. The paper gives a detailed account of the mathematical developments and the final expressions, including some illustrative examples.